Question

A brewer is trying to maximize the alcohol content of his new Stout. He experiments by varying the amount of grain added to each batch, with 3 different weights: 1 pound, 1.25 pounds, and 1.5 pounds. He run 5 replicates of each batch, and gets the following results:
1.0 lbs 1.25 lbs 1.5 lbs
5.12 5.11 6.03
5.34 5.53 5.58
5.17 4.18 5.74
4.58 5.45 6.19
5.10 4.69 6.06

What is the hypothesis the brewer is testing in this experiment?
Null Hypothesis


What are the 2 assumptions he must verify before proceeding?

What is your analysis of the impact of grain added to alcohol content at =0.05?

Answer 1

Here we will use one way anova

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha: At least one mean is different.

where is mean for 1 pounds

is mean for 1.25 pounds

is mean for 1.5 pounds

The 2 assumptions he must verify before proceeding are

All populations have a common variance and all samples are drawn independently of each other.

Now by using SPSS i'm analysing the data

Here factors are for 0-1 pounds

1-1.25 pounds

2-1.5 pounds.

Here test statistic is

F= MS(Between groups)/M.S(Within groups)

F= 1.335/0.154

F=8.697

P VALUE= 0.005 WHICH IS SMALLER THAN 0.05 LEVEL OF SIGNIFICANCE HENCE SIGNIFICANT.

CONCLUSION: SINCE P VALUE IS SIGNIFICANT WE REJECT NULL HYPOTHESIS H0 AND CONCLUDE THAT AT LEAST ONE MEAN IMPACT OF GRAIN ADDED TO ALCOHOL IS DIFFERENT.

I DID ABOVE TUKEYS TEST

(1.25 POUNDS VS 1.0 POUNDS) IS SIGNIFICANT P= 0.012

(1.25 POUNDS VS 1.5 POUNDS) IS SIGNIFICANT P=0.07